The harmonic index H (G) of a graph G is defined as the sum of the weights 2 du+dv of all edges uv of G, where du denotes the degree of a vertex u in G. In this paper, we determine (i) the trees of order n and m pendant vertices with the second smallest harmonic index, (ii) the trees of order n and diameter r with the smallest and the second smallest harmonic indices, and (iii) the trees of ord...

AIMS The significance of left ventricular hypertrophy in hypertension is well documented, being an independent risk factor for cardiovascular morbidity and mortality. Normal values for left ventricular mass and partition values for left ventricular hypertrophy come from measurements obtained by fundamental echocardiography. Secondary harmonic imaging improves definition of cardiac borders. We h...

The harmonic index of a graph G is defined as the sum of the weights 2 d(u) + d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this work, we present the minimum and maximum values of the harmonic index for connected graphs with girth at least k (k ≥ 3), and characterize the corresponding extremal graphs. Using this result, we obtain several relations between the h...

The harmonic index of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we give a sharp lower bound on the harmonic index of trees with a perfect matching in terms of the number of vertices. A sharp lower bound on the harmonic index of trees with a given size of matching is ...

The harmonic index H(G) of a graph G is defined as the sum of weights 2 d(u) + d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we first present a sharp lower bound on the harmonic index of unicyclic conjugated graphs (unicyclic graphs with a perfect matching). Also a sharp lower bound on the harmonic index of unicyclic graphs is given in terms of the ...

The harmonic index ) (G H , of a graph G is defined as the sum of weights 1 )) deg( ) (deg( 2   v u of all edges in ) (G E , where deg (u) denotes the degree of a vertex u in V(G). In this paper we define the harmonic polynomial of G as      ) ( 1 ) deg( ) deg( 2 ) , ( G E uv v u x x G H , where   1 0 ) ( ) , ( G H dx x G H . We present explicit formula for the values of harmonic polyn...

In this paper, we compute ABC index, Randic connectivity index, Sum connectivity index, GA index, Harmonic index, General Randic index of Triglyceride. AMS subject classification: